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Learning dynamical systems with biochemically informed neural ordinary differential equations
Luis L Fonseca1, Reinhard C Laubenbacher1, Lucas Böttcher2,1
1Laboratory for Systems Medicine, Department of Medicine, University of Florida, Gainesville, FL, USA.
Biorxiv : the Preprint Server for Biology
|June 5, 2026
Summary
We introduce biochemically informed neural ordinary differential equations (BINODEs) to model complex biological systems. This framework combines mechanistic structure with neural networks, improving interpretability and flexibility in dynamical systems modeling.
Area of Science:
- Computational Biology
- Systems Biology
- Machine Learning
Background:
- Ordinary differential equation (ODE) models are crucial for biochemical reactions but struggle with unknown process dynamics.
- Inferring functional forms of biological processes from data is challenging.
Purpose of the Study:
- To develop a novel framework, biochemically informed neural ordinary differential equations (BINODEs), for modeling biological dynamical systems.
- To integrate mechanistic stoichiometric structure with data-driven neural network flexibility.
Main Methods:
- Proposed BINODEs, a neural-ODE framework representing individual processes using neural networks.
- Mapped neural network process outputs to state derivatives via a linear layer, akin to a stoichiometric matrix.
- Incorporated biological side information like sign constraints and monotonicity assumptions.
Main Results:
- Characterized neural network process approximation properties for standard biochemical rate laws.
- Demonstrated BINODEs' ability to recover system trajectories and process-level structure.
- Validated the framework on Monod, Lotka-Volterra, pharmacokinetic, and ultradian endocrine models.
Conclusions:
- BINODEs offer a powerful compromise between mechanistic interpretability and data-driven modeling flexibility.
- The framework is suitable for partially known biochemical and biological dynamical systems.
- BINODEs enhance the modeling of complex biological systems with unknown components.
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